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#include "erfa.h"
void eraLtpecl(double epj, double vec[3])
/*
** - - - - - - - - - -
** e r a L t p e c l
** - - - - - - - - - -
**
** Long-term precession of the ecliptic.
**
** Given:
** epj double Julian epoch (TT)
**
** Returned:
** vec double[3] ecliptic pole unit vector
**
** Notes:
**
** 1) The returned vector is with respect to the J2000.0 mean equator
** and equinox.
**
** 2) The Vondrak et al. (2011, 2012) 400 millennia precession model
** agrees with the IAU 2006 precession at J2000.0 and stays within
** 100 microarcseconds during the 20th and 21st centuries. It is
** accurate to a few arcseconds throughout the historical period,
** worsening to a few tenths of a degree at the end of the
** +/- 200,000 year time span.
**
** References:
**
** Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession
** expressions, valid for long time intervals, Astron.Astrophys. 534,
** A22
**
** Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession
** expressions, valid for long time intervals (Corrigendum),
** Astron.Astrophys. 541, C1
**
** Copyright (C) 2013-2016, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
/* Obliquity at J2000.0 (radians). */
static const double eps0 = 84381.406 * ERFA_DAS2R;
/* Polynomial coefficients */
enum { NPOL = 4 };
static const double pqpol[2][NPOL] = {
{ 5851.607687,
-0.1189000,
-0.00028913,
0.000000101},
{-1600.886300,
1.1689818,
-0.00000020,
-0.000000437}
};
/* Periodic coefficients */
static const double pqper[][5] = {
{ 708.15,-5486.751211,-684.661560, 667.666730,-5523.863691},
{2309.00, -17.127623,2446.283880,-2354.886252, -549.747450},
{1620.00, -617.517403, 399.671049, -428.152441, -310.998056},
{ 492.20, 413.442940,-356.652376, 376.202861, 421.535876},
{1183.00, 78.614193,-186.387003, 184.778874, -36.776172},
{ 622.00, -180.732815,-316.800070, 335.321713, -145.278396},
{ 882.00, -87.676083, 198.296701, -185.138669, -34.744450},
{ 547.00, 46.140315, 101.135679, -120.972830, 22.885731}
};
static const int NPER = (int) ( sizeof pqper / 5 / sizeof (double) );
/* Miscellaneous */
int i;
double t, p, q, w, a, s, c;
/* Centuries since J2000. */
t = ( epj - 2000.0 ) / 100.0;
/* Initialize P_A and Q_A accumulators. */
p = 0.0;
q = 0.0;
/* Periodic terms. */
w = ERFA_D2PI*t;
for ( i = 0; i < NPER; i++ ) {
a = w/pqper[i][0];
s = sin(a);
c = cos(a);
p += c*pqper[i][1] + s*pqper[i][3];
q += c*pqper[i][2] + s*pqper[i][4];
}
/* Polynomial terms. */
w = 1.0;
for ( i = 0; i < NPOL; i++ ) {
p += pqpol[0][i]*w;
q += pqpol[1][i]*w;
w *= t;
}
/* P_A and Q_A (radians). */
p *= ERFA_DAS2R;
q *= ERFA_DAS2R;
/* Form the ecliptic pole vector. */
w = 1.0 - p*p - q*q;
w = w < 0.0 ? 0.0 : sqrt(w);
s = sin(eps0);
c = cos(eps0);
vec[0] = p;
vec[1] = - q*c - w*s;
vec[2] = - q*s + w*c;
}
/*----------------------------------------------------------------------
**
**
** Copyright (C) 2013-2016, NumFOCUS Foundation.
** All rights reserved.
**
** This library is derived, with permission, from the International
** Astronomical Union's "Standards of Fundamental Astronomy" library,
** available from http://www.iausofa.org.
**
** The ERFA version is intended to retain identical functionality to
** the SOFA library, but made distinct through different function and
** file names, as set out in the SOFA license conditions. The SOFA
** original has a role as a reference standard for the IAU and IERS,
** and consequently redistribution is permitted only in its unaltered
** state. The ERFA version is not subject to this restriction and
** therefore can be included in distributions which do not support the
** concept of "read only" software.
**
** Although the intent is to replicate the SOFA API (other than
** replacement of prefix names) and results (with the exception of
** bugs; any that are discovered will be fixed), SOFA is not
** responsible for any errors found in this version of the library.
**
** If you wish to acknowledge the SOFA heritage, please acknowledge
** that you are using a library derived from SOFA, rather than SOFA
** itself.
**
**
** TERMS AND CONDITIONS
**
** Redistribution and use in source and binary forms, with or without
** modification, are permitted provided that the following conditions
** are met:
**
** 1 Redistributions of source code must retain the above copyright
** notice, this list of conditions and the following disclaimer.
**
** 2 Redistributions in binary form must reproduce the above copyright
** notice, this list of conditions and the following disclaimer in
** the documentation and/or other materials provided with the
** distribution.
**
** 3 Neither the name of the Standards Of Fundamental Astronomy Board,
** the International Astronomical Union nor the names of its
** contributors may be used to endorse or promote products derived
** from this software without specific prior written permission.
**
** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
** POSSIBILITY OF SUCH DAMAGE.
**
*/
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